sm11 32

________________________________________________________________________
PROBLEM (11.32) Brace BD of the structure shown in Fig. P11.32 is a steel rod (E = 200
GPa and σy = 220 MPa) of square cross section (40 mm on a side). Determine the safety factor
ns against failure by buckling.
SOLUTION
1.4 m
B
10 kN
2
m
x
FBD
A 1
1
1
0: 10(3.4) (2) 0
2
AB
MF=− + =
∑DN, 24.04
BD
Fk
=
44 3
12 40 12 213.3 10 4
I
bmm== =× 32 40 40 1.6 10Amm=×= ×,
2000
11.5 173.9
11.5
IL
rmm
Ar
== = =
So,
22 9
22
(200 10 ) 65.27
( ) (173.9)
cr E
M
Pa
Lr
ππ
σ
×
== =
We have
cr pl
σ
σ < (solution is valid)
63
( ) 65.27 10 (1.6 10 ) 104.43
BD cr
Fk
−
=× ×= N
and
() 104.43 4.3
24.04
BD cr
sBD
F
nF ===
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